I believe that this was broken in the 12.6 release. I am seeing the same problem in Safari version 16.0 (17614.1.29.9.10). It has been driving me crazy since I routinely move tabs to new windows or between windows. The following screen captures shows the outcome of dragging this tab from the parent to a new window. Both the new window and its shadow in the parent window will update when you toggle between them.
You will see a similar behavior when you drag tabs between windows. The difference in that case is that the tab title is empty in the new window. I am assuming that this is a defect that came out of the tab grouping changes recently introduced.
Tabs do not leave first window entirely a… - Apple Community seems to be the same issue.